Optimal path of the simulation model in horticultural crop development and harvest period

A universally optimal path can greatly contribute to the simulation models in the horticultural crop development and harvest period, in order to efficiently utilize the agricultural resources during intelligent management. In this study, an optimal horticultural crop development and harvesting period simulation model was established to evaluate the relationship between crop growth and development, and the key meteorological factors (radiation and temperature). Four types of modeling methods were selected (temperature difference, accumulated temperature, physiological development time, product of thermal effectiveness, and photosynthetically active radiation). The experimental materials were taken as the cucumber ('Jinyou 35' and 'Jinsheng 206'), tomato ('Ruifen 882' and 'Provence'), celery ('Juventus'), spinach ('Daye'), parsley ('Siji'), tulip ('Pink impression', 'Daydream', 'Esmee' and 'Queen of Night'), and tea ('Longjing'). The observation data was obtained for the 58 groups of sowing stages over nine years from 2013 to 2022 (38 groups of early sowing and late sowing data were used to establish the model, and 21 groups of intermediate sowing data were used to the validate model). The key parameters of the model were then determined to integrate the simulation. Four approaches were used (average integration, maximum average integration, median integration, and stepwise regression integration) to ultimately determine the optimal simulation path for the model. The simulation was also conducted to clarify the significant impact of seasonal production capacity, stubble allocation, utilization efficiency of light and heat resources, and human factors on the actual cultivation of infinitely growing crops (cucumber, tomato, and tea) in the development period. The important model parameters were optimized in the development and harvest periods. A series of experiments were then carried out to verify the model. There were some outstanding features of the model as follows: To take the radiation and air temperature as the main driving variables, TE included two kinds of temperature response modes, two kinds of time scales, considering the difference in the simulation accuracy between the multi-model integration and single model, and the construction of characteristic module (harvest period module). The results showed that: 1) The root mean square errors (RMSE) of development and harvest simulation models were from 4.85 to 17.01 d on the different time scales, and the normalized root mean square errors (NRMSE) were from 10.65% to 16.31%. The RMSEs of development and harvest simulation models were from 0.50 to 17.08 d for the different varieties, and the NRMSEs were from 4.33% to 20.24%. The optimal development simulation model was the tulip, while the optimal harvest simulation model was the cucumber. The RMSEs of development and harvest simulation models were from 0.08 to 24.37 d for the different methods, and the NRMSEs were from 0.18% to 54.81%. 2) The hourly time scale was better than the daily one (RMSE and NRMSE difference values were 2.40 d, and 3.81%, respectively). Furthermore, the integration was superior to the single one (RMSE difference was 3.59 d, NRMSE difference was 6.28%) among the five types of modeling methods. The sine mode was superior to the linear one (RMSE difference was 0.52 d, and NRMSE difference was 0.73%) among the two types of temperature response modes. The leaf temperature was better than the air temperature (RMSE difference was 1.64 d, and NRMSE difference was 1.58%) among the two types of temperature forms. It was necessary to consider the effects of both the lower and upper limit temperatures simultaneously. The temperature response mode considering the biological lower limit and upper limit temperature was superior to the temperature response mode considering only the biological lower limit temperature (RMSE difference values were 0.10 and 0.39 d, respectively, whereas, NRMSE difference values were 0.13% and 0.82%, respectively) among the three types of extreme temperature responses. 3) Firstly, the model was established by selecting time scale, considering the sinusoidal temperature response mode of biological lower and upper limits, and leaf temperature form. Secondly, integration method optimized the development period (median integration) and harvesting period (stepwise regression integration) models. The finding can provide the theoretical basis and technical support for the intelligent management of the horticultural crops.